There are 180 oranges in a box. The table shows the distribution of the masses of these oranges.
| Mass (\(m\) g) | \(90<m\leq100\) | \(100<m\leq110\) | \(110<m\leq120\) | \(120<m\leq130\) | \(130<m\leq140\) |
|---|
| Frequency | \(10\) | \(28\) | \(51\) | \(45\) | \(48\) |
Calculate an estimate of the standard deviation of the masses.[1]
The weighing machine was faulty and overestimated each of the oranges by 5 g. Explain, with a reason, what will happen to the standard deviation.[2]
Explain why the range of the masses of oranges may not be 50 g.[1]
Roy says, “The modal class is the interval \(110<m\leq120\) but the modal mass may not be in the interval \(110<m\leq120\).” Is he correct? Give a reason for your answer.[2]